Here is where you are mistaken about all of these analogies to flying tea pots and leprechauns, evidence of absence is not absence of evidence, sure there is no physical evidence for God but it in no way follows that God does not exist because of that fact, it’s rather the evidence against something that we take into account to prove his being or his non being.
For example we have robust evidence that there are no trolls under bridge and we also have robust evidence that no such a flying teapot exists in our world it’s very easy to prove they do not exist, however there is not a shred of evidence that God does not exist and here is where your little childish examples fall flat.
There are many things for which there is no evidence for their non-existence. I am sure you and I could think of dozens in a matter of minutes.
I don't use this example to offend you, but consider the type of evidence required in order to prove there are no other humans in your home. You could attempt to monitor each room from each angle with cameras, you could remove all furnishings and all non-supportive structures, you could use various electromagnetic waves to document the regularity of the structure. All of this would have to be over an extended period of time, around the clock, until you come to realize that the only thing being demonstrated is that there is no one in the home when it is being observed. I illustrate this to show that in order to satisfy a negative proposition requires a certain amount of evidence, and even so, that evidence will never be satisfactory. Now think about the supernatural beings that the others have used as analogies. Easter bunnies, leprechauns, santa clauses, etc... are not normal beings which we encounter in our daily lives. These have properties which necessarily make them special, and are necessarily (for the sake of folklore) ill defined. We would have such a hard time negating the existence of physical beings which we are familiar with, how much harder would it be to disprove beings which are not constrained by what we understand as the physical world.
I don't believe in santa clauses, or easter bunnies, and it's not because I find the idea of those beings ridiculous. I don't believe in their existence because I don't yet have a reason to believe them. If you think about it, there are far too many propositions in the world, whether past or present, and in respect to the vast majority of them we would be on the same page. Just as you wouldn't turn your head every 4 seconds to catch some possible intruder because you have no reason to believe there is one to begin with... and as no one seriously proposes there are trolls under bridges, no one believes there's any reason to look for them.
Just to let you know I'm not trying to be difficult. There have been many cultures which formed a religion which worships the sun. The sun itself was their god, or representative of their god. With respect to the beliefs of those people, I could not say that I am an atheist. They would call the sun their god, I could look up and see the sun, and by their definitions their god exists and I could share that experience. I would not necessarily be an adherent to any other faith or beliefs that they would hold. We don't have to agree that their sun is supernatural or representative of chariot in the sky, because those beliefs would themselves need proof.
You may argue that it’s impossible to prove that something does not exist, then again this would be wrong because it’s very easy to prove something does not exist, for example I can prove there are no married bachelors.
The statement "there are no married bachelors" would not begin or end any sort of proof. The attribute of being married and the attribute of being a bachelor are mutually exclusive. Any two terms which are mutually exclusive by definition will work.
All the best,
Faysal